The proposed research will develop a general methodology for identification of quantitative trait loci (QTLs). Most methods still require special breeding programs, and because of this, they are applicable only in heavily manipulated situations such as plant or animal breeding. As-of-yet, there is no general method to map QTLs in either arbitrarily bred populations (for example, those in conservation genetic programs) or in populations that cannot be readily controlled (as in many human studies). This proposal addresses this deficiency and presents a general methodology that is not only applicable to arbitrarily bred populations, but is both statistically more powerful and has a wider inference space. Specifically, this research will develop the random model approach as a general methodology for QTL mapping by: 1). Developing the theory of an IBD-based random model approach for QTL analysis. IBD is the proportion of alleles that are identical- by-descent; 2). Developing a full maximum likelihood method to implement the random model methodology b) incorporating distributions of IBD matrices; 3). Investigating the Gibbs sampling algorithm and comparing its statistical powers and estimation errors (or confidence intervals) with the full maximum likelihood method; 4). Comparing powers and efficiencies of the random model with the fixed model through simulation studies; 5). Extending the IBD-based random model approach to QTL mapping for ordinal characters (e.g., disease traits); 6). Releasing a set of computer programs that implement the random model QTL mapping method